Raven is building a new planter for her class garden. 1.1 The base of her planter is \( 2 \frac{1}{2} \) feet by \( 2 \frac{1}{4} \) feet. What is the area of the base of the planter? 1.2 If the planter is \( \frac{2}{3} \) of a foot high, what volume soil does she need to fill the planter?

Let's solve Raven's planter problem step by step. ### 1.1 Calculating the Area of the Base The base of the planter is a rectangle with dimensions: - **Length:** \( 2 \frac{1}{2} \) feet - **Width:** \( 2 \frac{1}{4} \) feet First, convert these mixed numbers to improper fractions: \[ 2 \frac{1}{2} = \frac{5}{2} \quad \text{and} \quad 2 \frac{1}{4} = \frac{9}{4} \] Now, calculate the area: \[ \text{Area} = \text{Length} \times \text{Width} = \frac{5}{2} \times \frac{9}{4} = \frac{45}{8} \] Convert the improper fraction to a mixed number: \[ \frac{45}{8} = 5 \frac{5}{8} \text{ square feet} \] **Answer:** The area of the base is \( 5 \frac{5}{8} \) square feet. --- ### 1.2 Calculating the Volume of Soil Needed The height of the planter is \( \frac{2}{3} \) of a foot. To find the volume, multiply the area of the base by the height: \[ \text{Volume} = \text{Area} \times \text{Height} = \frac{45}{8} \times \frac{2}{3} \] Multiply the numerators and the denominators: \[ \text{Volume} = \frac{45 \times 2}{8 \times 3} = \frac{90}{24} \] Simplify the fraction: \[ \frac{90}{24} = \frac{15}{4} = 3 \frac{3}{4} \text{ cubic feet} \] **Answer:** Raven needs \( 3 \frac{3}{4} \) cubic feet of soil to fill the planter.